The city has to be right next to the water. Just the fat cross containing water doesn't count. So these work (city = X, water W, land = L):
LLW
LCL
LLL
LWL
LCL
LLL
but this doesn't:
WWWW
LLLW
LCLW
LLLW
WWWW
Buildings/techs/govs that help with food:
*Harbor, +1 food in all H2O tiles.
*Granary, city retains 50% of food in storage when it grows
*Non-despotism, no -1 penalty for tiles producing 3+ of food/shields/gold
*Agricultural civilization (C3C), irrigated deserts produce 2 food
*Railroad, irrigated tiles give +1 food in addition to what the irrigation already allows
*Aqueduct, allows a city without a river in the fat cross to grow beyond size 6
*Hospital, allows a city to grow beyond size 12
*Shakespeare's Theatre (Great Wonder), allows that one city to grow beyond size 12
*The Pyramids (Great Wonder), gives a Granary in every city you control on the same continent
*Longevity (Great Wonder), cities grow by 2 instead of 1 when the food meter is full
Agricultural might also give the center city tile +1 food, not sure about that off the top of my head. Certain luxuries (such as Wine) and bonus resources (such as fish) increase food production, as well.